LMFDB - L-function search results

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Lowest zero	Conductor	Analytic conductor	Central character	Analytic rank

Degree	Bad $p$	Root analytic conductor	Motivic weight	Spectral label

Root angle	Primitive	Origin	Exclude origin	Self-dual

Arithmetic

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Results (1-50 of 54 matches)

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Label	$\alpha$	$A$	$d$	$N$	$\chi$	$\mu$	prim	arith	$\operatorname{Arg}(\epsilon)$	$r$	First zero	Origin
1-297-297.104-r1-0-0	$31.9$	$31.9$	$1$	$3^{3} \cdot 11$	297.104	$1$	✓	✓	$-0.442$	$0$	$0.211221$	Character $\chi_{297}(104, \cdot)$
1-297-297.106-r1-0-0	$31.9$	$31.9$	$1$	$3^{3} \cdot 11$	297.106	$1$	✓	✓	$-0.459$	$0$	$1.17391$	Character $\chi_{297}(106, \cdot)$
1-297-297.112-r1-0-0	$31.9$	$31.9$	$1$	$3^{3} \cdot 11$	297.112	$1$	✓	✓	$0.0113$	$0$	$0.554220$	Character $\chi_{297}(112, \cdot)$
1-297-297.113-r1-0-0	$31.9$	$31.9$	$1$	$3^{3} \cdot 11$	297.113	$1$	✓	✓	$0.244$	$0$	$1.38295$	Character $\chi_{297}(113, \cdot)$
1-297-297.119-r1-0-0	$31.9$	$31.9$	$1$	$3^{3} \cdot 11$	297.119	$1$	✓	✓	$0.109$	$0$	$0.851225$	Character $\chi_{297}(119, \cdot)$
1-297-297.13-r1-0-0	$31.9$	$31.9$	$1$	$3^{3} \cdot 11$	297.13	$1$	✓	✓	$0.344$	$0$	$0.127146$	Character $\chi_{297}(13, \cdot)$
1-297-297.137-r1-0-0	$31.9$	$31.9$	$1$	$3^{3} \cdot 11$	297.137	$1$	✓	✓	$-0.405$	$0$	$0.352694$	Character $\chi_{297}(137, \cdot)$
1-297-297.139-r1-0-0	$31.9$	$31.9$	$1$	$3^{3} \cdot 11$	297.139	$1$	✓	✓	$0.00374$	$0$	$0.923035$	Character $\chi_{297}(139, \cdot)$
1-297-297.14-r1-0-0	$31.9$	$31.9$	$1$	$3^{3} \cdot 11$	297.14	$1$	✓	✓	$0.244$	$0$	$0.0252152$	Character $\chi_{297}(14, \cdot)$
1-297-297.142-r1-0-0	$31.9$	$31.9$	$1$	$3^{3} \cdot 11$	297.142	$1$	✓	✓	$0.435$	$0$	$0.981478$	Character $\chi_{297}(142, \cdot)$
1-297-297.146-r1-0-0	$31.9$	$31.9$	$1$	$3^{3} \cdot 11$	297.146	$1$	✓	✓	$-0.0519$	$0$	$0.866849$	Character $\chi_{297}(146, \cdot)$
1-297-297.151-r1-0-0	$31.9$	$31.9$	$1$	$3^{3} \cdot 11$	297.151	$1$	✓	✓	$-0.337$	$0$	$0.161895$	Character $\chi_{297}(151, \cdot)$
1-297-297.158-r1-0-0	$31.9$	$31.9$	$1$	$3^{3} \cdot 11$	297.158	$1$	✓	✓	$-0.281$	$0$	$0.921404$	Character $\chi_{297}(158, \cdot)$
1-297-297.160-r1-0-0	$31.9$	$31.9$	$1$	$3^{3} \cdot 11$	297.160	$1$	✓	✓	$-0.344$	$0$	$1.79764$	Character $\chi_{297}(160, \cdot)$
1-297-297.175-r1-0-0	$31.9$	$31.9$	$1$	$3^{3} \cdot 11$	297.175	$1$	✓	✓	$-0.101$	$0$	$1.00196$	Character $\chi_{297}(175, \cdot)$
1-297-297.178-r1-0-0	$31.9$	$31.9$	$1$	$3^{3} \cdot 11$	297.178	$1$	✓	✓	$-0.451$	$0$	$1.27732$	Character $\chi_{297}(178, \cdot)$
1-297-297.184-r1-0-0	$31.9$	$31.9$	$1$	$3^{3} \cdot 11$	297.184	$1$	✓	✓	$0.459$	$0$	$2.03442$	Character $\chi_{297}(184, \cdot)$
1-297-297.185-r1-0-0	$31.9$	$31.9$	$1$	$3^{3} \cdot 11$	297.185	$1$	✓	✓	$0.0720$	$0$	$0.510685$	Character $\chi_{297}(185, \cdot)$
1-297-297.191-r1-0-0	$31.9$	$31.9$	$1$	$3^{3} \cdot 11$	297.191	$1$	✓	✓	$-0.244$	$0$	$2.02671$	Character $\chi_{297}(191, \cdot)$
1-297-297.193-r1-0-0	$31.9$	$31.9$	$1$	$3^{3} \cdot 11$	297.193	$1$	✓	✓	$0.118$	$0$	$1.55034$	Character $\chi_{297}(193, \cdot)$
1-297-297.20-r1-0-0	$31.9$	$31.9$	$1$	$3^{3} \cdot 11$	297.20	$1$	✓	✓	$0.442$	$0$	$2.01658$	Character $\chi_{297}(20, \cdot)$
1-297-297.203-r1-0-0	$31.9$	$31.9$	$1$	$3^{3} \cdot 11$	297.203	$1$	✓	✓	$-0.109$	$0$	$0.371829$	Character $\chi_{297}(203, \cdot)$
1-297-297.205-r1-0-0	$31.9$	$31.9$	$1$	$3^{3} \cdot 11$	297.205	$1$	✓	✓	$-0.459$	$0$	$0.439493$	Character $\chi_{297}(205, \cdot)$
1-297-297.211-r1-0-0	$31.9$	$31.9$	$1$	$3^{3} \cdot 11$	297.211	$1$	✓	✓	$0.344$	$0$	$1.96326$	Character $\chi_{297}(211, \cdot)$
1-297-297.212-r1-0-0	$31.9$	$31.9$	$1$	$3^{3} \cdot 11$	297.212	$1$	✓	✓	$-0.0889$	$0$	$0.274169$	Character $\chi_{297}(212, \cdot)$
1-297-297.218-r1-0-0	$31.9$	$31.9$	$1$	$3^{3} \cdot 11$	297.218	$1$	✓	✓	$0.109$	$0$	$1.19821$	Character $\chi_{297}(218, \cdot)$
1-297-297.236-r1-0-0	$31.9$	$31.9$	$1$	$3^{3} \cdot 11$	297.236	$1$	✓	✓	$-0.0720$	$0$	$0.923661$	Character $\chi_{297}(236, \cdot)$
1-297-297.238-r1-0-0	$31.9$	$31.9$	$1$	$3^{3} \cdot 11$	297.238	$1$	✓	✓	$0.337$	$0$	$1.10000$	Character $\chi_{297}(238, \cdot)$
1-297-297.241-r1-0-0	$31.9$	$31.9$	$1$	$3^{3} \cdot 11$	297.241	$1$	✓	✓	$0.101$	$0$	$1.19916$	Character $\chi_{297}(241, \cdot)$
1-297-297.245-r1-0-0	$31.9$	$31.9$	$1$	$3^{3} \cdot 11$	297.245	$1$	✓	✓	$-0.0519$	$0$	$0.871749$	Character $\chi_{297}(245, \cdot)$
1-297-297.250-r1-0-0	$31.9$	$31.9$	$1$	$3^{3} \cdot 11$	297.250	$1$	✓	✓	$0.00374$	$0$	$0.382834$	Character $\chi_{297}(250, \cdot)$
1-297-297.257-r1-0-0	$31.9$	$31.9$	$1$	$3^{3} \cdot 11$	297.257	$1$	✓	✓	$0.0519$	$0$	$0.510722$	Character $\chi_{297}(257, \cdot)$
1-297-297.259-r1-0-0	$31.9$	$31.9$	$1$	$3^{3} \cdot 11$	297.259	$1$	✓	✓	$-0.344$	$0$	$0.129423$	Character $\chi_{297}(259, \cdot)$
1-297-297.274-r1-0-0	$31.9$	$31.9$	$1$	$3^{3} \cdot 11$	297.274	$1$	✓	✓	$-0.435$	$0$	$0.0789695$	Character $\chi_{297}(274, \cdot)$
1-297-297.277-r1-0-0	$31.9$	$31.9$	$1$	$3^{3} \cdot 11$	297.277	$1$	✓	✓	$-0.118$	$0$	$1.23298$	Character $\chi_{297}(277, \cdot)$
1-297-297.283-r1-0-0	$31.9$	$31.9$	$1$	$3^{3} \cdot 11$	297.283	$1$	✓	✓	$0.459$	$0$	$0.0494817$	Character $\chi_{297}(283, \cdot)$
1-297-297.284-r1-0-0	$31.9$	$31.9$	$1$	$3^{3} \cdot 11$	297.284	$1$	✓	✓	$0.405$	$0$	$1.63472$	Character $\chi_{297}(284, \cdot)$
1-297-297.290-r1-0-0	$31.9$	$31.9$	$1$	$3^{3} \cdot 11$	297.290	$1$	✓	✓	$0.0889$	$0$	$0.904428$	Character $\chi_{297}(290, \cdot)$
1-297-297.292-r1-0-0	$31.9$	$31.9$	$1$	$3^{3} \cdot 11$	297.292	$1$	✓	✓	$0.451$	$0$	$0.230690$	Character $\chi_{297}(292, \cdot)$
1-297-297.38-r1-0-0	$31.9$	$31.9$	$1$	$3^{3} \cdot 11$	297.38	$1$	✓	✓	$-0.405$	$0$	$2.28264$	Character $\chi_{297}(38, \cdot)$
1-297-297.40-r1-0-0	$31.9$	$31.9$	$1$	$3^{3} \cdot 11$	297.40	$1$	✓	✓	$0.337$	$0$	$1.59141$	Character $\chi_{297}(40, \cdot)$
1-297-297.43-r1-0-0	$31.9$	$31.9$	$1$	$3^{3} \cdot 11$	297.43	$1$	✓	✓	$0.101$	$0$	$1.45990$	Character $\chi_{297}(43, \cdot)$
1-297-297.47-r1-0-0	$31.9$	$31.9$	$1$	$3^{3} \cdot 11$	297.47	$1$	✓	✓	$0.281$	$0$	$1.16658$	Character $\chi_{297}(47, \cdot)$
1-297-297.5-r1-0-0	$31.9$	$31.9$	$1$	$3^{3} \cdot 11$	297.5	$1$	✓	✓	$-0.109$	$0$	$0.883643$	Character $\chi_{297}(5, \cdot)$
1-297-297.52-r1-0-0	$31.9$	$31.9$	$1$	$3^{3} \cdot 11$	297.52	$1$	✓	✓	$-0.337$	$0$	$0.890003$	Character $\chi_{297}(52, \cdot)$
1-297-297.59-r1-0-0	$31.9$	$31.9$	$1$	$3^{3} \cdot 11$	297.59	$1$	✓	✓	$0.0519$	$0$	$0.864242$	Character $\chi_{297}(59, \cdot)$
1-297-297.61-r1-0-0	$31.9$	$31.9$	$1$	$3^{3} \cdot 11$	297.61	$1$	✓	✓	$-0.0113$	$0$	$1.14675$	Character $\chi_{297}(61, \cdot)$
1-297-297.7-r1-0-0	$31.9$	$31.9$	$1$	$3^{3} \cdot 11$	297.7	$1$	✓	✓	$-0.125$	$0$	$0.620967$	Character $\chi_{297}(7, \cdot)$
1-297-297.76-r1-0-0	$31.9$	$31.9$	$1$	$3^{3} \cdot 11$	297.76	$1$	✓	✓	$-0.101$	$0$	$0.588794$	Character $\chi_{297}(76, \cdot)$
1-297-297.79-r1-0-0	$31.9$	$31.9$	$1$	$3^{3} \cdot 11$	297.79	$1$	✓	✓	$-0.451$	$0$	$0.151005$	Character $\chi_{297}(79, \cdot)$

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Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.